Logger pro graphs of a
tennis ball thrown up
and to the side
• Video findings:
2D motion
– The “Y” velocity (vy) changes with an acceleration
of about -10m/s2
– The “X” velocity (vx) has no acceleration and is at
constant speed
– The two are connected through time but that is
basically it
– At the top of the motion vx is the same vy is zero
but ay is still -10m/s2
A cannon fires a cannonball 135 m/s at a 16° angle.
1. What is the velocity in the vertical direction?
2. Using vertical velocity and acceleration how
long is the ball in the air?
3. What is the velocity in the horizontal direction?
4. Using the time in the air how far will
it go
A cannon fires a cannonball 135 m/s at a 16° angle.
1. What is the velocity in the vertical direction?
= = ∗ = . 2. Using vertical velocity and acceleration how
long is the ball in the air?
At ground
= = + + = + . + (−)
= . level at start
and end
3. What is the velocity in the horizontal direction?
= = ∗ = . 4. Using the time in the air how far will
it go
∆ = = . ∗ . = . m
vo
Vosin(θ)
θ
Vocos(θ)
Projectile Motion
Assumptions:
1. Acceleration is due to gravity, g, has
magnitude of 9.80 m/s2 and is always toward
earth (downward)
2. Effect of air resistance can be ignored
3. Rotation of earth can be ignored
The path of the object will be a parabola:
Perpendicular vectors act independently!!!
This means you can change one of the vectors
without changing the other.
Horizontal
Components
Vertical Component
Nothing to cause it to
accelerate so its
velocity remains
constant.
Gravity causes an
acceleration of
9.8 %⁄&'.
Velocity: (constant)
)* + = )+ cos /
Initial Velocity
)0 = )+ sin /
+
Final Velocity
)0 = )0 + 34
+
5
5
)0 = )0 + + 23∆7
Horizontal Distance:
8 = )4
Vertical Distance:
1 5
∆7 = )0 + 4 + :4
2
Ball rolls across table at constant speed of 4.50
m/s. How far does it travel from the edge of the
table if the table height is 1.25 m?
Ball rolls across table at constant speed of 4.50
m/s. How far does it travel from the edge of the
table if the table height is 1.25 m?
B-17 is flying at 375 km/h (104.167m/s). The
bombs travel a horizontal distance of 5,250 m.
What was the altitude of the plane at the time
they had the old "bombs away"?
B-17 is flying at 375 km/h. The bombs travel a
horizontal distance of 5,250 m. What was the
altitude of the plane at the time they had the old
"bombs away"?
A naval gun fires a projectile. The gun’s muzzle
velocity (so speed of the bullet) is 345 m/s at an
elevation of 32.0 °. What is the range of the shot?
A naval gun fires a projectile. The gun’s muzzle
velocity (so speed of the bullet) is 345 m/s at an
elevation of 32.0 °. What is the range of the shot?